Method for locating an object using a reference grid

ABSTRACT

A method for locating an object by a reference grid, the object moving in a plane parallel to or identical to that of the grid. When crossing of a line of the grid is detected by the object, its heading is determined and, as a function of the detection, probabilities of the thus crossed line being a horizontal line and a vertical line respectively are obtained. Displacement of the object is assessed from the probabilities obtained and a horizontal and vertical pitch of the grid. A position of the object is then updated from a position of the object determined during a last line crossing of the grid and the displacement thus assessed.

TECHNICAL FIELD

The present invention generally relates to the field of location andmore particularly that of locating inside buildings (so-called indoorlocation). The locating method according to the invention is applicablein particular to locating supermarket trolleys.

STATE OR PRIOR ART

Indoor location is a specific research field because of the absence ofsatellite radiolocation signals inside buildings. Numerous originalsolutions have been proposed in the literature and some of them giverise to actual devices.

Among the proposed solutions, one can recite in particular thoseresorting to power measurements of Wi-Fi access points, those resortingto UWB (Ultra Wide Band) transmitters or even those resorting toinertial techniques.

Indoor location from Wi-Fi access points implies a sufficient actualdensity of such access points, a condition which is not always fulfilledin practice. It also suffers from an insufficient accuracy.

UWB radiolocation techniques, with or without satellite hybridization,are relatively expensive since they require resorting to specifictransmitters.

The location using inertial systems (for example using MEMS gyroscopes)is liable to quick drifts over time and consequently requires frequentresettings.

A method for locating a supermarket trolley was proposed in theapplication WO-A-9959112. The trolley is equipped with a RFID tag whichcan be detected by detector matrices provided in the ground. Thislocating method however implies a very heavy infrastructure.

A method for locating a robot was proposed in Patent applicationKR-A-20110010422. The robot is equipped with an upwardly directed camerafilming the ceiling while the robot moves. The ceiling is provided witha bidimensional arrangement of orthogonal lines forming a grid. Thisgrid consists of so-called horizontal lines, spaced apart by a distanceL_(x), and so-called vertical lines, spaced apart by a distance L_(y).The distances L_(x) and L_(y) are assumed to be known.

Images captured by the camera are processed in real time and theposition of the robot is determined as a function of the line crossingof the grid. More precisely, each time the image centre crosses a lineof the grid, the robot coordinates are updated as follows:x _(i) =x _(i−1) +k _(x) L _(x)y _(i) =y _(i−1) +k _(y) L _(y)  (1)where (x_(i), y_(i)) are the robot coordinates in a horizontal planeduring the i^(th) line crossing, and k_(x), k_(y) assume their valuesamong the triplet {−1, 0, 1} as explained later. It is assumed that thecoordinates are defined with respect to an origin O in the horizontalplane and that the horizontal (resp. vertical) lines of the ceiling areparallel to the axis Ox (resp. Oy).

The values of k_(x), k_(y) are defined as follows:

-   -   k_(x)=1 (resp. k_(y)=1) if the image centre crosses a horizontal        line (resp. a vertical line) in the increasing x (resp. y)        direction;    -   k_(x)=0 (resp. k_(y)=0) if the image centre does not cross a        horizontal line (resp. a vertical line);    -   k_(x)=−1 (resp. k_(y)=−1) if the image centre crosses a        horizontal line (resp. a vertical line) in the decreasing x        (resp. y) direction;

FIG. 1 represents the principle of the locating method described in theaforesaid patent application.

The image captured by the camera is represented by a solid square 110,superimposed with the reference grid 100. The grid consists ofhorizontal lines 101 and vertical lines 102.

The image centre, indicated by the point P, conventionally defines thecurrent position of the robot. α_(i) represents the angle between thedirection of the robot movement and the (horizontal or vertical) linecrossed by the point P during the i^(th) crossing. If φ_(i) representsthe robot course with respect to the axis Ox, the latter can bedetermined from the angle α_(i) according to the different possiblecrossing situations:

-   -   a) k_(x)=1 and k_(y)=0, that is if the point P crosses a        horizontal line in the increasing x direction: φ_(i)=α_(i);    -   b) k_(x)=−1 and k_(y)=0, that is if the point P crosses a        horizontal line in the increasing x direction: φ_(i)=−α_(i);    -   c) k_(x)=0 and k_(y)=1, that is if the point P crosses a        vertical line in the increasing y direction: φ_(i)=π/2−α_(i);    -   d) k_(x)=0 and k_(y)=−1, that is if the point P crosses a        vertical line in the decreasing y direction: φ_(i)=3π/2−α_(i).

At each line crossing, the robot selects from hypotheses (a) to (d), theone that minimizes the variation in orientation between two successivecrossings, in other words the angular deviation |φ_(i)−φ_(i−1)|. Thevalues of k_(x), k_(y) corresponding to this minimum are deduced and thecoordinates of the robot are updated by means of the expression (1).

This locating method however has a number of drawbacks. First, itrequires an expensive equipment and complex image processings. Then, andabove all, it can lead to disastrous results in case of a quick turn(rotation by more than 90°) or even a reverse movement of the robot.Indeed, in this case, the condition of minimizing the angular deviation|φ_(i)−φ_(i−1)| between two successive crossings is not relevant. Giventhat it is not possible to distinguish a crossing of a horizontal linefrom a crossing of a vertical line, the entire subsequent trajectory isaffected by an error of at least 90°.

The object of the present invention is consequently to provide alocating method by means of a reference grid which is particularlysimple and robust.

DISCLOSURE OF THE INVENTION

The present invention is defined by a method for locating an object bymeans of a reference grid, the object moving in a plane parallel to oridentical to that of the grid, said grid being defined by a plurality ofso-called horizontal lines, aligned along a first direction and aplurality of so-called vertical lines, aligned along a second directiondistinct from the first one, the vertical lines being separated by afirst distance along the first direction and the horizontal lines beingseparated by a second distance along the second direction. According tothis method each time the object crosses a line of the grid,

-   -   the heading of the object is determined with respect to a        reference direction;    -   as a function of the course thus determined, the probabilities        p(dy_(i)|φ_(i)), p(dx_(i)|φ_(i)) of the line thus crossed being        respectively a horizontal line and a vertical line of the grid,        are obtained when the object moves in the direction given by the        heading;    -   from said probabilities and the first and second distances, the        displacement (        ,        ) of the object since the last time it crossed the line of the        grid is assessed;    -   the position of the object is updated from the displacement thus        assessed.

In a conventional application, the first and second directions areorthogonal.

If the first direction is selected as said reference direction, theprobability p(dx_(i)|φ_(i)) of the crossed line being a vertical line isdetermined by

${p\left( {d\; x_{i}} \middle| \varphi_{i} \right)} = \frac{\tan(\theta)}{{\tan(\theta)} + {{\tan\left( \varphi_{i} \right)}}}$and the probability p(dy_(i)|φ_(i)) of the crossed line being ahorizontal line is determined by

${{p\left( {d\; y_{i}} \middle| \varphi_{i} \right)} = \frac{{\tan\left( \varphi_{i} \right)}}{{\tan(\theta)} + {{\tan\left( \varphi_{i} \right)}}}},$where tan (θ)=L_(y)/L_(x), L_(x) and L_(y) being respectively the firstand second distances and φ_(i), being the heading.

The displacement of the object is then assessed by means of

=sgn(cos φ_(i))p(dx_(i)|φ_(i))L_(x) and

=sgn(sin φ_(i))p(dy_(i)|φ_(i))L_(y) where sgn(·) is the signum functionand φ_(i) is the heading.

The position (

,

) of the object can be updated according to

=

+

and

=

+

where (

,

) is the position of the object obtained the last time the objectcrossed a line of the grid and (

,

) is the displacement assessed since this last time.

Typically, the object is equipped with a first sensor suitable fordetecting a line crossing of the grid. This first sensor can be anoptical sensor or an accelerometer.

The object can further include course measuring means comprising asecond sensor suitable for providing the orientation of the object and athird sensor suitable for giving the direction of its movement.

The second sensor can be a magnetometer or a gyroscope.

The third sensor can be of the same type as the first one and beprovided on the object in the proximity of the first sensor, the orderof detecting the line crossing by the first and third sensors providingthe direction of movement.

The third sensor can be a Doppler sensor.

When the object is equipped with wheels, the third sensor can besuitable for providing the direction of the rotation of said wheels.

In an application of the invention, the object is a supermarket trolley.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 represents the principle of a locating method using a referencegrid known from prior art;

FIG. 2 represents the flow diagram of the locating method according toone embodiment of the present invention;

FIG. 3A represents the trajectory of an object which is obtained thanksto the locating method according to the embodiment of FIG. 2, in theabsence of angular noise and wrong crossing detection;

FIG. 3B represents the trajectory of the object by means of the samelocating method but under deteriorated conditions.

DETAILED DISCLOSURE OF PARTICULAR EMBODIMENTS

The problem of locating an object using a reference grid will beconsidered again.

By location, it is meant herein the determination of the object positionand more precisely, the determination of the coordinates of this objectin a bidimensional reference frame. This bidimensional reference framedefines the plane wherein the object moves. The plane referred to can bethat of the reference grid or a plane parallel thereto. The locatingmethod according to the invention has within its scope the case wherethe position is determined by the object itself (in the strict sense,the method is then a “positioning” method) and the case where thisposition is determined by a system external to the object (locationmethod strictly speaking). The term location is herein intended in itsgeneral acceptance and covers either case.

The object can be a priori any object, for example an industrial robot,a supermarket trolley or an autonomous vehicle. The reference grid canin this case be provided on the ground or on the ceiling of a building.In another context of application, the object can be a pen, a light pen,an optical mouse or the like. The reference grid is then provided on asupport such as a paper sheet or a graphical tablet.

The reference grid can also be made in multiple ways. In the firstabovementioned application type, it can result from a pavement on theground or a pavement of a false-ceiling. In the second application type,it can be obtained by means of a printing onto the support or a display(LCD panel for example).

In any case, the object is provided with a first sensor capable ofdetecting lines forming the grid. This sensor can be an optical one, inwhich case the detection of the line crossing is obtained for example bymeans of a grey level or colour change in the centre of the image.Alternatively, this sensor can be an accelerometer or a shock sensorwhen the lines of the grid are formed in a relief or hollow manner (caseof a pavement on the ground or a pattern on a support), the line beingdetected by means of the vibration generated when the object crosses it.This sensor can also be an inductive one when the grid consists of anarray of conductors buried or present in the ground. It will begenerally understood that the type of sensor will be a function of thetype of reference grid being used.

The reference grid consists of a set of so-called horizontal lines,aligned along a first direction and a second set of so-called verticallines, aligned along a second direction, distinct from the first one.The vertical lines are spaced apart by a distance L_(x) along the firstdirection and the horizontal lines are spaced by a distance L_(y) alongthe second direction. The first and second directions are preferablyorthogonal. In the following, the reference frame (O, u_(x), u_(y)) willbe considered where the origin O is located in the plane where theobject moves and u_(x), u_(y) are the unit vectors respectively directedin the first and second directions.

The object is further equipped with heading measuring means enabling thedirection of movement of the object to be determined in the referenceframe in question. These means can comprise a second sensor capable ofdetermining the orientation of the object as well as a third sensorgiving the direction of its movement. It should be noted that this thirdsensor is optional if the object can only move in a single direction(forward direction only for example).

The second sensor can consist of a magnetometer (giving the orientationof the object with respect to the terrestrial magnetic field or anartificial magnetic field), a gyroscope, a camera suitable for detectingvisual marks in a building, an array of antennas suitable for detectingthe angle of arrival of a signal emitted by a beacon, etc.

The third sensor can be made for example by a wheel rotation sensor whenthe object is equipped therewhith, a Doppler sensor or even anaccelerometer. Advantageously, the third sensor will be identical to thefirst one and located in the proximity thereof, the direction ofmovement being then determined by the order wherein the line crossing isdetected by the first and third sensors.

The second and third sensors can be multiple ones and their respectiveoutputs averaged so as to improve the signal to noise ratio of theheading measurement.

Other embodiments of the heading measuring means could be contemplatedby those skilled in the art without departing from the scope of thepresent invention.

The locating method according to the invention is based on aprobabilistic approach of line crossings of the reference grid, from aprevious knowledge of the direction of movement of the object.

The originality of this method lies in not trying to find, at each linecrossing, whether the crossed line is horizontal or vertical(deterministic approach) but in taking advantage of the great number ofline crossed by a segment of the object trajectory.

More precisely, if it is assumed that the i^(th) line crossing has justbeen detected and if p(dx_(i)|φ_(i)), resp. p(dy_(i)|φ_(i)), representsthe conditional probability that the crossed line is vertical, resp.horizontal, given that the direction of movement is at an angle φ_(i)with the axis Ox (that is with the first direction), there are thefollowing relationships:

$\begin{matrix}{{{{p\left( {d\; x_{i}} \middle| \varphi_{i} \right)} + {p\left( {d\; y_{i}} \middle| \varphi_{i} \right)}} = 1}{\frac{p\left( {d\; y_{i}} \middle| \varphi_{i} \right)}{p\left( {d\; x_{i}} \middle| \varphi_{i} \right)} = \frac{\lambda_{x}\left( \varphi_{i} \right)}{\lambda_{y}\left( \varphi_{i} \right)}}} & (2)\end{matrix}$where λ_(x)(φ_(i)), λ_(y)(φ_(i)) are respectively the densities of thehorizontal and vertical lines when the object moves in the direction ofmovement. The axis of movement is noted Δ(φ_(i)).

When the vertical and horizontal lines are orthogonal, it can be shownthat the ratio of densities can be simply expressed as:

$\begin{matrix}{{\frac{\lambda_{x}\left( \varphi_{i} \right)}{\lambda_{y}\left( \varphi_{i} \right)} = {\frac{{\tan\left( \varphi_{i} \right)}/L_{y}}{1/L_{x}} = {\frac{L_{x}{\tan\left( \varphi_{i} \right)}}{L_{y}} = \frac{\tan\left( \varphi_{i} \right)}{\tan(\theta)}}}}{{{with}\mspace{14mu}{\tan(\theta)}} = {\frac{L_{y}}{L_{x}}.}}} & (3)\end{matrix}$

The expression (3) is intuitively understood since if the object movesalong the axis Δ(φ_(i)) of (Δ_(x), Δ_(x) tan(φ_(i))) in the referenceframe (O, u_(x), u_(y)), the average number of vertical lines crossedduring this movement will be Δ_(x)/L_(x) whereas the average number ofhorizontal lines crossed during the same movement will be Δ_(x)tan(φ_(i))/L_(y).

If it is assumed that 0≦φ_(i)<π/2, the movement between two linecrossings can be assessed by:

=p(dx _(i)|φ_(i))L _(x)

=p(dy _(i)|φ_(i))L _(y)  (4)that is, taking account of (2) and (3):

$\begin{matrix}{{{\hat{dx}}_{i} = {{\frac{\tan(\theta)}{{\tan(\theta)} + {\tan\left( \varphi_{i} \right)}}L_{x}} = {\frac{L_{y}}{L_{y} + {L_{x}{\tan\left( \varphi_{i} \right)}}}L_{x}}}}{{\hat{dy}}_{i} = {{\frac{\tan\left( \varphi_{i} \right)}{{\tan(\theta)} + {\tan\left( \varphi_{i} \right)}}L_{y}} = {\frac{L_{x}{\tan\left( \varphi_{i} \right)}}{L_{y} + {L_{x}{\tan\left( \varphi_{i} \right)}}}L_{y}}}}} & (5)\end{matrix}$

If the functions ƒ_(x) and ƒ_(y) are respectively defined by:

$\begin{matrix}{{f_{x}\left( \varphi_{i} \right)} = {{p\left( {dx}_{i} \middle| \varphi_{i} \right)} = \frac{\tan(\theta)}{{\tan(\theta)} + {{\tan\left( \varphi_{i} \right)}}}}} & (6) \\{{f_{y}\left( \varphi_{i} \right)} = {{p\left( {dy}_{i} \middle| \varphi_{i} \right)} = \frac{{\tan\left( \varphi_{i} \right)}}{{\tan(\theta)} + {{\tan\left( \varphi_{i} \right)}}}}} & (7)\end{matrix}$the displacement (

,

) of the object is assessed for the different ranges of φ_(i) asfollows:

-   -   0≦φ_(i)<π/2        =ƒ_(x)(φ_(i))L _(x);        =ƒ_(y)(φ_(i))L _(y)  (8)    -   π/2≦φ_(i)<π        =−ƒ_(x)(φ_(i))L _(x);        =ƒ_(y)(φ_(i))L _(y)  (9)    -   −π≦φ_(i)<−π/2        =−ƒ_(x)(φ_(i))L _(x);        =−ƒ_(y)(φ_(i))L _(y)  (10)    -   −π/2≦φ_(i)<0        =ƒ_(x)(φ_(i))L _(x);        =−ƒ_(y)(φ_(i))L _(y)  (11)

In any case, it will be noted that the displacement of the object isgiven by

=sgn(cos φ_(i))ƒ_(x)(φ_(i))L_(x) and

=sgn(sin φ_(i))ƒ_(y)(φ_(i))L_(y) where sgn(·) is the signum function(equal to −1 for a negative number and equal to +1 for a positivenumber).

The position (

,

) of the object in the reference frame (O, u_(x), u_(y)) upon detectingthe i^(th) crossing is then assessed by means of:

=

+

=

+

  (12)where (

,

) was the position of the object assessed during the previous crossing.

FIG. 2 represents the flow diagram of the locating method according toone embodiment of the invention.

The reference grid is defined by the vectors u_(x) and u_(y)respectively giving the first and second directions, as well as thedistances L_(x) and L_(y), in the meaning defined above. The distancesL_(x) and L_(y) are assumed to be known.

In step 210, the position of the object is initialized by

=x₀,

=y₀. In practice, this initializing step could be triggered when theobject passes at a predetermined point of a known position (for examplethe entrance of a building). The previous passing of the object throughthis point could incidentally condition the implementation of thelocating method.

When a line crossing is detected using the first sensor, in 220, it isdetermined in 225 the direction of movement of the object using headingmeasuring means. This direction is conventionally defined by the angleφ_(i) with the first direction.

Then, it is determined in which angular range the direction of movementis.

If, in 230, the angle φ_(i) is such that 0≦φ_(i)<π/2, in other words ifthe object moves in the positive x direction and that of positive y, theobject position is updated in 235 by means of the expressions (8) and(12), that is:

=

+ƒ_(x)(φ_(i))L _(x)

=

+ƒ_(y)(φ_(i))L _(y)  (13)

If not, the method proceeds to 240.

If in 240, the angle φ_(i) is such that π/2≦φ_(i)<π, in other words, ifthe object moves in the negative x direction and that of positive y, theposition of the object is updated in 245 by means of the expressions (9)and (12), that is:

=

−ƒ_(x)(φ_(i))L _(x)

=

+ƒ_(y)(φ_(i))L _(y)  (14)

If not, the method proceeds to 250.

If in 250, the angle φ_(i) is such that −π≦φ_(i)<−π/2, in other words,if the object moves in the negative x direction and that of negative y,the position of the object is updated in 255 by means of the expressions(10) and (12), that is:

=

−ƒ_(x)(φ_(i))L _(x)

=

−ƒ_(y)(φ_(i))L _(y)  (15)

If not, the angle φ_(i) is such that −π/2≦φ_(i)<0, that is the objectmoves in the negative x direction and that of negative y, the positionof the object is updated in 265 by means of the expressions (10) and(12), that is:

=

+ƒ_(x)(φ_(i))L _(x)

=

−ƒ_(y)(φ_(i))L _(y)  (16)

Then we go back to the step of crossing detection in 220.

The values ƒ_(x)(φ_(i)), ƒ_(y)(φ_(i)) or, possibly, the valuesƒ_(x)(φ_(i))L_(x) ƒ_(y)(φ_(i))L_(y) can be stored in a table and read asa function of the heading φ_(i). Alternatively, these values can becalculated at each line crossing.

The locating method can further include calibration phases at regularintervals or when the object passes through a known position.

The position calculation can be performed by a processor equipping theobject or remotely by a system external to the object. In the lattercase, the line crossing information as well as the course φ_(i) aretransmitted by the object to the system in question.

FIG. 3A represents in dash line the actual trajectory, 310, of an objectmoving with respect to a reference grid. The trajectory assessed bymeans of the previously described locating method is represented insolid line, 320. It has been assumed here that the course measured wasthe actual course of the object and that the line crossing detection wasnot affected by errors.

It is noticed that the assessed trajectory is very close to the actualtrajectory. Even in the case of a quick turn of the object (cusp Q), thelocating method enables a good approximation of the actual trajectory tobe achieved, without the occurrence of a disastrous error.

FIG. 3B represents the trajectory assessed by the same locating methodbut under deteriorated conditions. More precisely, it has been assumedhere that the heading measurement was affected by an angular noise witha standard deviation of 10° and that the line crossing detectionoperated with a false alarm rate of 14% and a non-detection rate of 10%.By false alarm, it is meant that a line crossing is detected whereas itis not present and by non-detection, it is meant that a line crossing bythe object is not detected.

It is noticed that despite the deteriorated operating conditions, thelocating method provides an acceptable assessment of the actualtrajectory. It is consequently robust and does not lead to disastrouserrors.

The invention claimed is:
 1. A method for locating an object by areference grid, the object moving in a plane parallel to or identical tothat of the grid, the grid being defined by a plurality of horizontallines aligned along a first direction and a plurality of vertical linesaligned along a second direction distinct from the first direction, thevertical lines being separated by a first distance, L_(x), along thefirst direction and the horizontal lines being separated by a seconddistance, L_(y), along the second direction, the method comprising, eachtime the object crosses at least one line of the grid: determining aheading, φ_(i), of the object with respect to a reference direction;obtaining, as a function of the determined heading, probabilitiesp(dy_(i)|φ_(i)), p(dx_(i)|φ_(i)), of the at least one line of the gridcrossed by the object being respectively a horizontal line of the gridand a vertical line of the grid, when the object moves in the headingdirection, φ_(i), where dy_(i) is a displacement of the object in thesecond direction, and dx_(i) is a displacement of the object in thefirst direction; assessing, from the probabilities p(dy_(i)|φ_(i)),p(dx_(i)|φ_(i)), the first distance, L_(x), and the second distance,L_(y), a displacement, (

,

), of the object since a most recent time the object crossed the atleast one line of the grid; and updating a position, ({circumflex over(x)}_(i), ŷ_(i)), of the object in the reference grid from the assesseddisplacement, (

,

).
 2. The locating method according to claim 1, wherein the first andsecond directions are orthogonal.
 3. The locating method according toclaim 1, wherein when the first direction is selected as the referencedirection, the probability p(dx_(i)|φ_(i)) of the at least one crossedline being a vertical line is determined by${{p\left( {d\; x_{l}} \middle| \varphi_{l} \right)} = \frac{\tan(\theta)}{{\tan(\theta)} + {{\tan\left( \varphi_{i} \right)}}}},$and the probability p(dy_(i)|φ_(i)) of the crossed line being ahorizontal line is determined by${{p\left( {d\; y_{l}} \middle| \varphi_{l} \right)} = \frac{\tan\left( \varphi_{i} \right)}{{\tan(\theta)} + {{\tan\left( \varphi_{i} \right)}}}},$where tan(θ)=L_(y)/L_(x).
 4. The locating method according to claim 2,wherein, the first direction being selected as the reference direction,the displacement of the object is assessed by

=sgn(cos φ_(i))p(dx₁|φ_(i))L_(x) and

=sgn(sin φ_(i))p(dy_(i)|φ_(i))L_(y) where sgn(·) is the signum function.5. The locating method according to claim 4, wherein the position,({circumflex over (x)}_(i), ŷ_(i)), of the object is updated accordingto {circumflex over (x)}_(i)=

+

and ŷ_(i)=

+

, where (

,

) is the position of the object obtained the last time the objectcrossed a line of the grid and (

,

) is the displacement assessed since the last time.
 6. The locatingmethod according to claim 1, wherein the object includes a first sensorconfigured for detecting a line crossing of the grid.
 7. The locatingmethod according to claim 6, wherein the first sensor is an opticalsensor.
 8. The locating method according to claim 6, wherein the firstsensor is an accelerometer.
 9. The locating method according to claim 6,wherein the object includes heading measuring means comprising a secondsensor configured to provide orientation of the object and a thirdsensor configured to give a direction of its movement.
 10. The locatingmethod according to claim 9, wherein the second sensor is amagnetometer.
 11. The locating method according to claim 10, wherein thesecond sensor is a gyroscope.
 12. The locating method according to claim9, wherein the third sensor is of same type as the first sensor and isprovided on the object in proximity of the first sensor, an order ofdetecting the line crossing by the first and third sensors providing thedirection of movement.
 13. The locating method according to claim 9,wherein the third sensor is a Doppler sensor.
 14. The locating methodaccording to claim 9, wherein the object includes wheels and the thirdsensor provides a direction of rotation of the wheels.
 15. The locatingmethod according to claim 1, wherein the object is a supermarkettrolley.